Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 5 - The Integral - Chapter Review Exercises - Page 278: 32


$$y= t^3+\sin t+12$$

Work Step by Step

Given$$ \frac{d y}{d t}=3 t^{2}+\cos t, \quad y(0)=12$$ Since :\begin{align*} y&= \int (3 t^{2}+\cos t) dt\\ &= t^3+\sin t +c \end{align*} at $t= 0,\ \ \ y= 12 $, then $c= 12$, hence $$y= t^3+\sin t+12$$
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